1)Prem Lam is establishing an investment portfolio that will include stock and bond funds. She has $1720,000 to invest, and he does not want the portfolio to include more than 75% stocks. Prem does not want the portfolio to include less than 45% bonds as well. The average annual return for the stock fund he plans to invest in is 28%, whereas the average annual return for the bond fund is 16%. He further estimates that the most he could lose in the next year in the stock fund is 25%, whereas the most she could lose in the bond fund is 15%. To reduce his risk, he wants to limit his potential maximum losses to $120,000.
Formulate a linear programming model for this problem that will maximize his returns on the portfolio.
2)Dorian Auto manufacturers luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, Dorian Auto has embarked on a ambitious TV advertising campaign and has decided to purchase 1-minute commercial spots on two types of programs; comedy shows and football games. Each comedy commercial is seen by 7 million high income women and 2 million high income men. Each football commercial is seen by 3 million high-income women and 11 million high-income men. A 1-minute comedy ad costs $40,000, and a 1-minute football ad costs $90,000. Dorian would like the commercials to be seen by at least 25 million high-income women and 20 million high-income men.
Use linear programming to determine how Dorian Auto can meet its advertising requirements at minimum cost
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